Abstract

This paper develops a systematic and formal approach to dimensional reduction of electromagnetic
boundary value problems. The approach is based on the concept of continuous symmetry,
and the definitions and the mathematical structures used are conceptually distinct
and completely coordinate-free and independent of dimensions. The approach leads to
sufficient conditions for when a boundary value problem can be solved as a lower-dimensional
one and it shows how to systematically formulate the lower-dimensional problems. The
symmetries are described with Lie groups that are products of connected 1-D Lie groups.